Show that `(4)/(12.18) - (4.7)/(12.18.24) + (4.7.10)/(12.18.24.30) - …..= 3 root(3) (9/4) - 47/12`

Show that (5)/(6.12) + (5.8)/(6.12.18) + (5.8.11)/(6.12.18.24) + ….. = (3root(3)(4) -4)/(6)

Show that (3)/(4.8)-(3.5)/(4.8.12) + (3.5.7)/(4.8.12.16) - …… = sqrt(2/3) -3/4

Add: (5)/(12) and ((-7))/(18)

(4)/(1.3)-(6)/(2.4)+(12)/(5.7)-(14)/(6.8)+….=

(3)/(4.8)+(3.5)/(4.8.12)+(3.5.7)/(4.8.12.16)+….=

Compare (-4)/(9) and (-7)/(12) .

5/8+3/4-7/(12) is equal to: (a) (15)/(24) (b) (17)/(24) (c) (19)/(24) (d) (21)/(24)

Express as like fractions: (5)/(18), (7)/(12), (5)/(6)

Write four more rational numbers in each of the following patterns : (i) (-3)/5 , (-6)/10 , (-9)/15 , (-12)/20,..... (ii) (-1)/4 , (-2)/8, (-3)/12,...... (iii) (-1)/6, 2/(-12), 3/(-18), 4/(-24),....... (iv) (-2)/3 , 2/(-3) , 4/(-6), 6/-9,.......

Simplify each of the following: (i) 124-(12-2) * 9 (ii) (13+7) * (9-4) -18 (iii) 210-(14-4) * (18+2) - 10